Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.lang.*;
import static java.lang.System.*;

public class C {
public static void main(String[] args){
Scanner sc= new Scanner(in);
int n=sc.nextInt();
int h=sc.nextInt();
double area=(1.0*h/2)/n;
double x1=0,x2=0;
double m1=0,m2=0;
for(int i=0;i<n-1;i++)
{
	if(x1==0)
	{
		x1=Math.sqrt(2*area*h);
		out.println(x1);
        m1=x1/h;
    }
	else
	{
     x2=Math.sqrt((x1/m1)*(area*2+m1*x1));
     out.println(x2);
     m2=x2*m1/x1;
     m1=m2;
     x1=x2;

	}
}







}
}